Late time approaches to the Hubble tension deforming $H(z)$, worsen the growth tension

Understand

Many late time approaches for the solution of the Hubble tension use late time smooth deformations of the Hubble expansion rate $H(z)$ of the Planck18/$\Lambda$CDM best fit to match the locally measured value of $H_0$ while effectively keeping the comoving distance to the last scattering surface and $\Omega_{0m} h^2$ fixed to maintain consistency with Planck CMB measurements.

• A well known problem of these approaches is that they worsen the fit to low $z$ distance probes.
• Here we show that another problem of these approaches is that they worsen the level of the $\Omega_{0m}-\sigma_8$ growth tension.
• We use the generic class of CPL parametrizations corresponding to evolving dark energy equation of state parameter $w(z)=w_0+w_1\frac{z}{1+z}$ with local measurements $H_0$ prior and identify the pairs $(w_0, w_1)$ that satisfy this condition.